Problem: Reduce to lowest terms: $- \dfrac{9}{2} \div \dfrac{2}{9} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{2}{9}$ is $ \dfrac{9}{2}$ Therefore: $ - \dfrac{9}{2} \div \dfrac{2}{9} = - \dfrac{9}{2} \times \dfrac{9}{2} $ $ \phantom{- \dfrac{9}{2} \times \dfrac{9}{2}} = \dfrac{-9 \times 9}{2 \times 2} $ $ \phantom{- \dfrac{9}{2} \times \dfrac{9}{2}} = \dfrac{-81}{4} $